Overview
- Acts as a perfect book for Graduate-level Fixed-Point Theory
- Covers all major Fixed-Point theories in detail
- Introduces Fixed-Point Theory and correlates it to several topics in Analysis
- Includes supplementary material: sn.pub/extras
Part of the book series: Universitext (UTX)
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About this book
This text provides an introduction to some of the best-known fixed-point theorems, with an emphasis on their interactions with topics in analysis. The level of exposition increases gradually throughout the book, building from a basic requirement of undergraduate proficiency to graduate-level sophistication. Appendices provide an introduction to (or refresher on) some of the prerequisite material and exercises are integrated into the text, contributing to the volume’s ability to be used as a self-contained text. Readers will find the presentation especially useful for independent study or as a supplement to a graduate course in fixed-point theory.
The material is split into four parts: the first introduces the Banach Contraction-Mapping Principle and the Brouwer Fixed-Point Theorem, along with a selection of interesting applications; the second focuses on Brouwer’s theorem and its application to John Nash’s work; the third applies Brouwer’s theorem to spaces of infinite dimension; and the fourth rests on the work of Markov, Kakutani, and Ryll–Nardzewski surrounding fixed points for families of affine maps.Similar content being viewed by others
Keywords
Table of contents (13 chapters)
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Introduction to Fixed Points
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From Brouwer to Nash
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Beyond Brouwer: Dimension = ∞
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Fixed Points for Families of Maps
Reviews
“The chapters provide models for students to appreciate the art of a well-thought out seminar talk … on a particular topic or theme. There are also a variety of exercises integrated into the lectures, ‘to encourage active participation’, which allow the text to be used for a course or an independent study. … The book appears to be written to engage a young audience, yet there is more in it to provide pleasure to mathematicians further on in their career.” (Tushar Das, Maa Reviews, maa.org, October, 2016)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: A Fixed-Point Farrago
Authors: Joel H. Shapiro
Series Title: Universitext
DOI: https://doi.org/10.1007/978-3-319-27978-7
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-27976-3Published: 31 May 2016
Softcover ISBN: 978-3-319-80251-0Published: 30 May 2018
eBook ISBN: 978-3-319-27978-7Published: 23 May 2016
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XIV, 221
Number of Illustrations: 8 b/w illustrations
Topics: Analysis, Numerical Analysis